7. Systems of Equations & Matrices

For Exercises 11–22, use Cramer's Rule to solve each system. $\begin{cases}2x = 3y + 2 \\5x = 51 - 4y\end{cases}$

In Exercises 23–30, use expansion by minors to evaluate each determinant. $\begin{vmatrix}3 & 0 & 0 \\2 & 1 & -5 \\2 & 5 & -1\end{vmatrix}$

Evaluate each determinant.

Evaluate each determinant.

In Exercises 23–30, use expansion by minors to evaluate each determinant. $\begin{vmatrix}3 & 1 & 0 \\-3 & 4 & 0 \\-1 & 3 & -5\end{vmatrix}$

Evaluate each determinant.

In Exercises 23–30, use expansion by minors to evaluate each determinant. $\begin{vmatrix}0.5 & 7 & 5 \\0.5 & 3 & 9 \\0.5 & 1 & 3\end{vmatrix}$

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. $\begin{vmatrix}-3 & 4 & -5 \\5 & -2 & 0 \\8 & -1 & 3\end{vmatrix}$

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. $\begin{vmatrix}1 & 5 & 6 \\1 & 4 & 5 \\1 & 9 & 10\end{vmatrix}$

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. $\begin{vmatrix}0.5 & 7 & 5 \\0.5 & 3 & 9 \\0.5 & 1 & 3\end{vmatrix}$

Evaluate each determinant.

In Exercises 37–44, use Cramer's Rule to solve each system. $\begin{cases}x + y + z = 0 \\2x - y + z = -1 \\-x + 3y - z = -8\end{cases}$

Evaluate each determinant.

In Exercises 37–44, use Cramer's Rule to solve each system. $\begin{cases}4x - 5y - 6z = -1 \\x - 2y - 5z = -12 \\2x - y = 7\end{cases}$

Evaluate each determinant.